The fundamental principle of Graph Neural Networks (GNNs) is to exploit the structural information of the data by aggregating the neighboring nodes using a `graph convolution' in conjunction with a suitable choice for the network architecture, such as depth and activation functions. Therefore, understanding the influence of each of the design choice on the network performance is crucial. Convolutions based on graph Laplacian have emerged as the dominant choice with the symmetric normalization of the adjacency matrix as the most widely adopted one. However, some empirical studies show that row normalization of the adjacency matrix outperforms it in node classification. Despite the widespread use of GNNs, there is no rigorous theoretical study on the representation power of these convolutions, that could explain this behavior. Similarly, the empirical observation of the linear GNNs performance being on par with non-linear ReLU GNNs lacks rigorous theory. In this work, we theoretically analyze the influence of different aspects of the GNN architecture using the Graph Neural Tangent Kernel in a semi-supervised node classification setting. Under the population Degree Corrected Stochastic Block Model, we prove that: (i) linear networks capture the class information as good as ReLU networks; (ii) row normalization preserves the underlying class structure better than other convolutions; (iii) performance degrades with network depth due to over-smoothing, but the loss in class information is the slowest in row normalization; (iv) skip connections retain the class information even at infinite depth, thereby eliminating over-smoothing. We finally validate our theoretical findings numerically and on real datasets such as Cora and Citeseer.
The message-passing mechanism helps Graph Neural Networks (GNNs) achieve remarkable results on various node classification tasks. Nevertheless, the recursive nodes fetching and aggregation in message-passing cause inference latency when deploying GNNs to large-scale graphs. One promising inference acceleration direction is to distill the GNNs into message-passing-free student multi-layer perceptrons (MLPs). However, the MLP student cannot fully learn the structure knowledge due to the lack of structure inputs, which causes inferior performance in the heterophily and inductive scenarios. To address this, we intend to inject structure information into MLP-like students in low-latency and interpretable ways. Specifically, we first design a Structure-Aware MLP (SA-MLP) student that encodes both features and structures without message-passing. Then, we introduce a novel structure-mixing knowledge distillation strategy to enhance the learning ability of MLPs for structure information. Furthermore, we design a latent structure embedding approximation technique with two-stage distillation for inductive scenarios. Extensive experiments on eight benchmark datasets under both transductive and inductive settings show that our SA-MLP can consistently outperform the teacher GNNs, while maintaining faster inference as MLPs. The source code of our work can be found in https://github.com/JC-202/SA-MLP.
The recent years we have seen the rise of graph neural networks for prediction tasks on graphs. One of the dominant architectures is graph attention due to its ability to make predictions using weighted edge features and not only node features. In this paper we analyze, theoretically and empirically, graph attention networks and their ability of correctly labelling nodes in a classic classification task. More specifically, we study the performance of graph attention on the classic contextual stochastic block model (CSBM). In CSBM the nodes and edge features are obtained from a mixture of Gaussians and the edges from a stochastic block model. We consider a general graph attention mechanism that takes random edge features as input to determine the attention coefficients. We study two cases, in the first one, when the edge features are noisy, we prove that the majority of the attention coefficients are up to a constant uniform. This allows us to prove that graph attention with edge features is not better than simple graph convolution for achieving perfect node classification. Second, we prove that when the edge features are clean graph attention can distinguish intra- from inter-edges and this makes graph attention better than classic graph convolution.
Graph neural networks (GNNs) hold the promise of learning efficient representations of graph-structured data, and one of its most important applications is semi-supervised node classification. However, in this application, GNN frameworks tend to fail due to the following issues: over-smoothing and heterophily. The most popular GNNs are known to be focused on the message-passing framework, and recent research shows that these GNNs are often bounded by low-pass filters from a signal processing perspective. We thus incorporate high-frequency information into GNNs to alleviate this genetic problem. In this paper, we argue that the complement of the original graph incorporates a high-pass filter and propose Complement Laplacian Regularization (CLAR) for an efficient enhancement of high-frequency components. The experimental results demonstrate that CLAR helps GNNs tackle over-smoothing, improving the expressiveness of heterophilic graphs, which adds up to 3.6% improvement over popular baselines and ensures topological robustness.
Recently, implicit graph neural networks (GNNs) have been proposed to capture long-range dependencies in underlying graphs. In this paper, we introduce and justify two weaknesses of implicit GNNs: the constrained expressiveness due to their limited effective range for capturing long-range dependencies, and their lack of ability to capture multiscale information on graphs at multiple resolutions. To show the limited effective range of previous implicit GNNs, We first provide a theoretical analysis and point out the intrinsic relationship between the effective range and the convergence of iterative equations used in these models. To mitigate the mentioned weaknesses, we propose a multiscale graph neural network with implicit layers (MGNNI) which is able to model multiscale structures on graphs and has an expanded effective range for capturing long-range dependencies. We conduct comprehensive experiments for both node classification and graph classification to show that MGNNI outperforms representative baselines and has a better ability for multiscale modeling and capturing of long-range dependencies.
The pretasks are mainly built on mutual information estimation, which requires data augmentation to construct positive samples with similar semantics to learn invariant signals and negative samples with dissimilar semantics in order to empower representation discriminability. However, an appropriate data augmentation configuration depends heavily on lots of empirical trials such as choosing the compositions of data augmentation techniques and the corresponding hyperparameter settings. We propose an augmentation-free graph contrastive learning method, invariant-discriminative graph contrastive learning (iGCL), that does not intrinsically require negative samples. iGCL designs the invariant-discriminative loss (ID loss) to learn invariant and discriminative representations. On the one hand, ID loss learns invariant signals by directly minimizing the mean square error between the target samples and positive samples in the representation space. On the other hand, ID loss ensures that the representations are discriminative by an orthonormal constraint forcing the different dimensions of representations to be independent of each other. This prevents representations from collapsing to a point or subspace. Our theoretical analysis explains the effectiveness of ID loss from the perspectives of the redundancy reduction criterion, canonical correlation analysis, and information bottleneck principle. The experimental results demonstrate that iGCL outperforms all baselines on 5 node classification benchmark datasets. iGCL also shows superior performance for different label ratios and is capable of resisting graph attacks, which indicates that iGCL has excellent generalization and robustness. The source code is available at https://github.com/lehaifeng/T-GCN/tree/master/iGCL.
Heterogeneous Information Network (HIN) is essential to study complicated networks containing multiple edge types and node types. Meta-path, a sequence of node types and edge types, is the core technique to embed HINs. Since manually curating meta-paths is time-consuming, there is a pressing need to develop automated meta-path generation approaches. Existing meta-path generation approaches cannot fully exploit the rich textual information in HINs, such as node names and edge type names. To address this problem, we propose MetaFill, a text-infilling-based approach for meta-path generation. The key idea of MetaFill is to formulate meta-path identification problem as a word sequence infilling problem, which can be advanced by Pretrained Language Models (PLMs). We observed the superior performance of MetaFill against existing meta-path generation methods and graph embedding methods that do not leverage meta-paths in both link prediction and node classification on two real-world HIN datasets. We further demonstrated how MetaFill can accurately classify edges in the zero-shot setting, where existing approaches cannot generate any meta-paths. MetaFill exploits PLMs to generate meta-paths for graph embedding, opening up new avenues for language model applications in graph analysis.
Recent work on Graph Neural Networks has demonstrated that self-supervised pretraining can further enhance performance on downstream graph, link, and node classification tasks. However, the efficacy of pretraining tasks has not been fully investigated for downstream large knowledge graph completion tasks. Using a contextualized knowledge graph embedding approach, we investigate five different pretraining signals, constructed using several graph algorithms and no external data, as well as their combination. We leverage the versatility of our Transformer-based model to explore graph structure generation pretraining tasks (i.e. path and k-hop neighborhood generation), typically inapplicable to most graph embedding methods. We further propose a new path-finding algorithm guided by information gain and find that it is the best-performing pretraining task across three downstream knowledge graph completion datasets. While using our new path-finding algorithm as a pretraining signal provides 2-3% MRR improvements, we show that pretraining on all signals together gives the best knowledge graph completion results. In a multitask setting that combines all pretraining tasks, our method surpasses the latest and strong performing knowledge graph embedding methods on all metrics for FB15K-237, on MRR and Hit@1 for WN18RRand on MRR and hit@10 for JF17K (a knowledge hypergraph dataset).
Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph-label consistency is a shortcoming. Then, we study heterophily from the perspective of post-aggregation node similarity and define new homophily metrics, which are potentially advantageous compared to existing ones. Based on this investigation, we prove that some harmful cases of heterophily can be effectively addressed by local diversification operation. Then, we propose the Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation, diversification and identity channels node-wisely to extract richer localized information for diverse node heterophily situations. ACM is more powerful than the commonly used uni-channel framework for node classification tasks on heterophilic graphs and is easy to be implemented in baseline GNN layers. When evaluated on 10 benchmark node classification tasks, ACM-augmented baselines consistently achieve significant performance gain, exceeding state-of-the-art GNNs on most tasks without incurring significant computational burden.
Large-scale graph training is a notoriously challenging problem for graph neural networks (GNNs). Due to the nature of evolving graph structures into the training process, vanilla GNNs usually fail to scale up, limited by the GPU memory space. Up to now, though numerous scalable GNN architectures have been proposed, we still lack a comprehensive survey and fair benchmark of this reservoir to find the rationale for designing scalable GNNs. To this end, we first systematically formulate the representative methods of large-scale graph training into several branches and further establish a fair and consistent benchmark for them by a greedy hyperparameter searching. In addition, regarding efficiency, we theoretically evaluate the time and space complexity of various branches and empirically compare them w.r.t GPU memory usage, throughput, and convergence. Furthermore, We analyze the pros and cons for various branches of scalable GNNs and then present a new ensembling training manner, named EnGCN, to address the existing issues. Our code is available at https://github.com/VITA-Group/Large_Scale_GCN_Benchmarking.
Graph neural networks (GNNs) have shown remarkable performance on diverse graph mining tasks. Although different GNNs can be unified as the same message passing framework, they learn complementary knowledge from the same graph. Knowledge distillation (KD) is developed to combine the diverse knowledge from multiple models. It transfers knowledge from high-capacity teachers to a lightweight student. However, to avoid oversmoothing, GNNs are often shallow, which deviates from the setting of KD. In this context, we revisit KD by separating its benefits from model compression and emphasizing its power of transferring knowledge. To this end, we need to tackle two challenges: how to transfer knowledge from compact teachers to a student with the same capacity; and, how to exploit student GNN's own strength to learn knowledge. In this paper, we propose a novel adaptive KD framework, called BGNN, which sequentially transfers knowledge from multiple GNNs into a student GNN. We also introduce an adaptive temperature module and a weight boosting module. These modules guide the student to the appropriate knowledge for effective learning. Extensive experiments have demonstrated the effectiveness of BGNN. In particular, we achieve up to 3.05% improvement for node classification and 6.35% improvement for graph classification over vanilla GNNs.
Graph Neural Networks (GNNs) have shown exceptional performance in the task of link prediction. Despite their effectiveness, the high latency brought by non-trivial neighborhood data dependency limits GNNs in practical deployments. Conversely, the known efficient MLPs are much less effective than GNNs due to the lack of relational knowledge. In this work, to combine the advantages of GNNs and MLPs, we start with exploring direct knowledge distillation (KD) methods for link prediction, i.e., predicted logit-based matching and node representation-based matching. Upon observing direct KD analogs do not perform well for link prediction, we propose a relational KD framework, Linkless Link Prediction (LLP), to distill knowledge for link prediction with MLPs. Unlike simple KD methods that match independent link logits or node representations, LLP distills relational knowledge that is centered around each (anchor) node to the student MLP. Specifically, we propose rank-based matching and distribution-based matching strategies that complement each other. Extensive experiments demonstrate that LLP boosts the link prediction performance of MLPs with significant margins, and even outperforms the teacher GNNs on 7 out of 8 benchmarks. LLP also achieves a 70.68x speedup in link prediction inference compared to GNNs on the large-scale OGB dataset.
Graph Convolutional Network (GCN) has exhibited strong empirical performance in many real-world applications. The vast majority of existing works on GCN primarily focus on the accuracy while ignoring how confident or uncertain a GCN is with respect to its predictions. Despite being a cornerstone of trustworthy graph mining, uncertainty quantification on GCN has not been well studied and the scarce existing efforts either fail to provide deterministic quantification or have to change the training procedure of GCN by introducing additional parameters or architectures. In this paper, we propose the first frequentist-based approach named JuryGCN in quantifying the uncertainty of GCN, where the key idea is to quantify the uncertainty of a node as the width of confidence interval by a jackknife estimator. Moreover, we leverage the influence functions to estimate the change in GCN parameters without re-training to scale up the computation. The proposed JuryGCN is capable of quantifying uncertainty deterministically without modifying the GCN architecture or introducing additional parameters. We perform extensive experimental evaluation on real-world datasets in the tasks of both active learning and semi-supervised node classification, which demonstrate the efficacy of the proposed method.
Message passing neural networks (MPNNs) learn the representation of graph-structured data based on graph original information, including node features and graph structures, and have shown astonishing improvement in node classification tasks. However, the expressive power of MPNNs is upper bounded by the first-order Weisfeiler-Leman test and its accuracy still has room for improvement. This work studies how to improve MPNNs' expressiveness and generalizability by fully exploiting graph original information both theoretically and empirically. It further proposes a new GNN model called INGNN (INformation-enhanced Graph Neural Network) that leverages the insights to improve node classification performance. Extensive experiments on both synthetic and real datasets demonstrate the superiority (average rank 1.78) of our INGNN compared with state-of-the-art methods.
In recent years, graph representation learning has gained significant popularity, which aims to generate node embeddings that capture features of graphs. One of the methods to achieve this is employing a technique called random walks that captures node sequences in a graph and then learns embeddings for each node using a natural language processing technique called Word2Vec. These embeddings are then used for deep learning on graph data for classification tasks, such as link prediction or node classification. Prior work operates on pre-collected temporal graph data and is not designed to handle updates on a graph in real-time. Real world graphs change dynamically and their entire temporal updates are not available upfront. In this paper, we propose an end-to-end graph learning pipeline that performs temporal graph construction, creates low-dimensional node embeddings, and trains multi-layer neural network models in an online setting. The training of the neural network models is identified as the main performance bottleneck as it performs repeated matrix operations on many sequentially connected low-dimensional kernels. We propose to unlock fine-grain parallelism in these low-dimensional kernels to boost performance of model training.
How can we solve semi-supervised node classification in various graphs possibly with noisy features and structures? Graph neural networks (GNNs) have succeeded in many graph mining tasks, but their generalizability to various graph scenarios is limited due to the difficulty of training, hyperparameter tuning, and the selection of a model itself. Einstein said that we should "make everything as simple as possible, but not simpler." We rephrase it into the careful simplicity principle: a carefully-designed simple model can surpass sophisticated ones in real-world graphs. Based on the principle, we propose SlimG for semi-supervised node classification, which exhibits four desirable properties: It is (a) accurate, winning or tying on 10 out of 13 real-world datasets; (b) robust, being the only one that handles all scenarios of graph data (homophily, heterophily, random structure, noisy features, etc.); (c) fast and scalable, showing up to 18 times faster training in million-scale graphs; and (d) interpretable, thanks to the linearity and sparsity. We explain the success of SlimG through a systematic study of the designs of existing GNNs, sanity checks, and comprehensive ablation studies.
Since most scientific literature data are unlabeled, this makes unsupervised graph-based semantic representation learning crucial. Therefore, an unsupervised semantic representation learning method of scientific literature based on graph attention mechanism and maximum mutual information (GAMMI) is proposed. By introducing a graph attention mechanism, the weighted summation of nearby node features make the weights of adjacent node features entirely depend on the node features. Depending on the features of the nearby nodes, different weights can be applied to each node in the graph. Therefore, the correlations between vertex features can be better integrated into the model. In addition, an unsupervised graph contrastive learning strategy is proposed to solve the problem of being unlabeled and scalable on large-scale graphs. By comparing the mutual information between the positive and negative local node representations on the latent space and the global graph representation, the graph neural network can capture both local and global information. Experimental results demonstrate competitive performance on various node classification benchmarks, achieving good results and sometimes even surpassing the performance of supervised learning.
In this paper, we propose a novel way of representing graphs for processing in Graph Neural Networks. We reduce the dimensionality of the input data by using Random Indexing, a Vector Symbolic Architectural framework; we implement a new trainable neural layer, also inspired by Vector Symbolic Architectures; we leverage the sparseness of the incoming data in a Sparse Neural Network framework. Our experiments on a number of publicly available datasets and standard benchmarks demonstrate that we can reduce the number of parameters by up to two orders of magnitude. We show how this parsimonious approach not only delivers competitive results but even improves performance for node classification and link prediction. We find that this holds in particular for cases where the graph lacks node features.
Recent years have witnessed great success in handling graph-related tasks with Graph Neural Networks (GNNs). Despite their great academic success, Multi-Layer Perceptrons (MLPs) remain the primary workhorse for practical industrial applications. One reason for this academic-industrial gap is the neighborhood-fetching latency incurred by data dependency in GNNs, which make it hard to deploy for latency-sensitive applications that require fast inference. Conversely, without involving any feature aggregation, MLPs have no data dependency and infer much faster than GNNs, but their performance is less competitive. Motivated by these complementary strengths and weaknesses, we propose a Graph Self-Distillation on Neighborhood (GSDN) framework to reduce the gap between GNNs and MLPs. Specifically, the GSDN framework is based purely on MLPs, where structural information is only implicitly used as prior to guide knowledge self-distillation between the neighborhood and the target, substituting the explicit neighborhood information propagation as in GNNs. As a result, GSDN enjoys the benefits of graph topology-awareness in training but has no data dependency in inference. Extensive experiments have shown that the performance of vanilla MLPs can be greatly improved with self-distillation, e.g., GSDN improves over stand-alone MLPs by 15.54% on average and outperforms the state-of-the-art GNNs on six datasets. Regarding inference speed, GSDN infers 75X-89X faster than existing GNNs and 16X-25X faster than other inference acceleration methods.
Self-supervised learning (SSL) for graph neural networks (GNNs) has attracted increasing attention from the graph machine learning community in recent years, owing to its capability to learn performant node embeddings without costly label information. One weakness of conventional SSL frameworks for GNNs is that they learn through a single philosophy, such as mutual information maximization or generative reconstruction. When applied to various downstream tasks, these frameworks rarely perform equally well for every task, because one philosophy may not span the extensive knowledge required for all tasks. To enhance the task generalization across tasks, as an important first step forward in exploring fundamental graph models, we introduce PARETOGNN, a multi-task SSL framework for node representation learning over graphs. Specifically, PARETOGNN is self-supervised by manifold pretext tasks observing multiple philosophies. To reconcile different philosophies, we explore a multiple-gradient descent algorithm, such that PARETOGNN actively learns from every pretext task while minimizing potential conflicts. We conduct comprehensive experiments over four downstream tasks (i.e., node classification, node clustering, link prediction, and partition prediction), and our proposal achieves the best overall performance across tasks on 11 widely adopted benchmark datasets. Besides, we observe that learning from multiple philosophies enhances not only the task generalization but also the single task performances, demonstrating that PARETOGNN achieves better task generalization via the disjoint yet complementary knowledge learned from different philosophies. Our code is publicly available at https://github.com/jumxglhf/ParetoGNN.